This paper discusses the technical challenges and trade-offs tied to design of medium frequency transformers for medium-voltage high-power applications and emerging solid state transformers. A dedicated design optimization algorithm is used to generate the set of all feasible transformer designs for the given electric requirements, originating from a modular DC-DC solid state transformer, and taking into account different geometry ratios, materials and operating frequencies. All possible design choice variations are compared in terms of maximum achievable efficiency, gravimetric and volumetric power density, identifying design limits for a given set of input parameters. Impact of modularity and choice of operating frequency directly related to selected semiconductors, reveal interesting trends that can aid overall solid state transformer design optimization.